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Treasury Bill Yield Day Count Across a Leap Year

Article Quant Q&A · Author: Yippie McSmashmouth
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Summary

The document examines a Treasury bill bought in late 2019 and maturing in early 2020. It calculates the days to maturity and price using a 360-day discount convention, then finds that annualizing the bill’s return with 365 days does not match the quoted yield. Using 366 days does match, raising the question of whether a leap year affects the calculation when the holding period spans both calendar years.

The accepted explanation attributes the result to the Treasury bill’s ACT/ACT convention: the yield basis is generally 365, but uses 366 when the year following the original issue date includes February 29. Under this rule, the relevant basis is not simply determined by the share of the holding period spent in each calendar year. The example explains the discrepancy for this bill, while users should verify the applicable day-count terms for other securities and conventions.

Key ideas

  • The bill’s price calculation uses a 360-day discount basis, while its yield uses a separate annualization basis.
  • Using 365 days fails to reproduce the quoted yield in the leap-year example.
  • The cited Treasury convention uses 366 when the year after the original issue date includes February 29.
  • The day-count basis is tied to the convention rather than the fraction of the holding period in each year.
  • Day-count rules should be checked for the specific security and calculation.

Tags

Fixed incomeStatistics
Full text
# Computing T-Bill Yield across leap year boundary


# Computing T-Bill Yield across leap year boundary












Consider this T-Bill (912796TE9) that was purchased on 2019-10-30 and matures on 2020-02-06:

I'm trying to work through some of the basics of the yield calculation.

The days until maturity is 99. (`2020-02-06 minus 2019-10-30`). That's easy enough.

The price is 99.563575. That's equal to `100 - ((discount) * (99/360))`. Again, pretty straightforward.

Where I'm running into trouble is the yield. According to this page we should compute:

```
yield = ((100-price)/price) * (365/daysLeft)
```

By my calculations, that generates a yield of around 1.616095%. But as you can see from the screenshot, the actual yield is 1.620522%. So I'm off.

Now it turns out, if I plug 366 into the equation instead of 365, I get the correct result. Why is that? Presumably it has something to do with 2020 being a leap year. But a good fraction of the holding period takes place in 2019 which is not a leap year. What's the rule on this? If any fraction of the holding period until maturity touches a leap year then 366 shall be used?

## Answer by oronimbus (score 4, accepted)

https://quant.stackexchange.com/a/49476

Due to the leap year 366 days need to be used here to match UST conventions (which is ACT/ACT). In this case it doesn't matter whether your interest period extends to only 1 day after the 29th of February or, e.g., 200. In fact if you look at the daycount description of the bill it says:

> "the day count basis for price and yield calculations is 365 depending on the number of actual days in year counting forward from the Original Issue Date. The basis will usually be 365 but if the year following the issue date includes February 29th then it's 366".

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.